U.S. patent application number 09/761132 was filed with the patent office on 2002-01-03 for apparatus for analyzing samples using combined thermal wave and x-ray reflectance measurements.
Invention is credited to Opsal, Jon, Rosencwaig, Allan.
Application Number | 20020001364 09/761132 |
Document ID | / |
Family ID | 26885034 |
Filed Date | 2002-01-03 |
United States Patent
Application |
20020001364 |
Kind Code |
A1 |
Opsal, Jon ; et al. |
January 3, 2002 |
Apparatus for analyzing samples using combined thermal wave and
x-ray reflectance measurements
Abstract
This invention provides a measurement device that includes both
an X-ray reflectometer and a thermal or plasma wave measurement
module for determining the characteristics of a sample. Preferably,
these two measurement modules are combined into a unitary apparatus
and arranged to be able to take measurements at the same location
on the wafer. A processor will receive data from both modules and
combine that data to resolve ambiguities about the characteristics
of the sample. The processor can be part of the device or separate
therefrom as long as the measurement data is transferred to the
processor.
Inventors: |
Opsal, Jon; (Livermore,
CA) ; Rosencwaig, Allan; (Danville, CA) |
Correspondence
Address: |
Michael A. Stallman
STALLMAN & POLLOCK LLP
Suite 290
121 Spear Street
San Francisco
CA
94105
US
|
Family ID: |
26885034 |
Appl. No.: |
09/761132 |
Filed: |
January 16, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60189334 |
Mar 14, 2000 |
|
|
|
Current U.S.
Class: |
378/88 ;
378/86 |
Current CPC
Class: |
G01N 23/20 20130101 |
Class at
Publication: |
378/88 ;
378/86 |
International
Class: |
G01N 023/201 |
Claims
What is claimed is:
1. A unitary apparatus for evaluating a sample comprising: (a) a
first measurement module including: (i) means for inducing a
periodic localized excitation at the surface of the sample; (ii)
means for directing a first probe beam of radiation within a
portion of the area periodically excited in a manner such that the
first probe beam reflects from the surface of the sample; (iii)
means for measuring the periodic variations of the reflected first
probe beam induced by said periodic excitation to generate first
output signals; (b) a second measurement module including: (i)
means for generating a second probe beam, said second probe beam
having X-ray wavelengths; (ii) means for directing said second
probe beam onto the surface of said sample; (iii) a detector for
measuring the intensity of X-rays reflected from said sample to
generate second output signals; and (c) a processor for evaluating
the sample based on a combination of the first and second output
signals.
2. An apparatus as recited in claim 1 wherein said means for
measuring the intensity of X-rays includes a photodiode
detector.
3. An apparatus as recited in claim 1 wherein said first probe beam
is generated by a laser.
4. An apparatus as recited in claim 1 wherein said means for
measuring the first probe beam measures periodic changes in the
magnitude or phase of the beam.
5. A method of evaluating a sample comprising the steps of: (a)
obtaining a first set of measurements by: (i) inducing a periodic
localized excitation on the surface of the sample; (ii) directing a
first probe beam of radiation within a portion of the area
periodically excited in a manner such that the first probe beam
reflects from the surface of the sample; and (iii) measuring the
intensity variations of the reflected first probe beam resulting
from periodic changes of the sample induced by said periodic
excitation to generate first output signals; and (b) obtaining a
second set of measurements by: (i) generating a second probe beam
of X-rays; (ii) directing said second probe beam onto the surface
of said sample; (iii) measuring the intensity of X-rays as
reflected from said sample to generate second output signals; and
(c) evaluating the sample based on a combination of the first and
second output signals.
6. A method as recited in claim 5 wherein said step of evaluating
the sample includes using either of the first or second output
signals to characterize one parameter of the sample and wherein the
other output signals are used to further characterize the sample
with said one parameter being treated as a known parameter.
7. A method as recited in claim 5 wherein said step of evaluating
the sample includes using the second output signal to characterize
the density of a sample layer and wherein the first output signals
are used to further characterize the sample with said layer density
being treated as a known parameter.
8. A method as recited in claim 5 wherein said step of evaluating
the sample includes using the second output signal to characterize
the thickness of a sample layer and wherein the first output
signals are used to further characterize the sample with said layer
thickness being treated as a known parameter.
9. A method as recited in claim 5 wherein said measuring of the
intensity of X-rays includes using a photodiode detector.
10. A method as recited in claim 5 wherein said first probe beam of
radiation is generated by a laser.
11. A method as recited in claim 5 wherein the periodic variations
in the magnitude and/or phase of the first probe beam are
measured.
12. A method of evaluating characteristics of a sample comprising
the steps of: periodically exciting a region on the surface of the
sample; monitoring the modulated optical reflectivity induced by
said periodic excitation and generating first output signals in
response thereto; directing a probe beam of X-ray radiation onto
the same region on the sample surface; monitoring the non-modulated
reflected power of the X-ray probe beam and generating second
output signals in response thereto; and evaluating the
characteristics of the sample based on a combination of the first
and second output signals.
13. A method as recited in claim 12 wherein said step of evaluating
the characteristics of the sample includes using either of the
first or second output signals to characterize one parameter of the
sample and wherein the other output signals are used to further
characterize the sample with said one parameter being treated as a
known parameter.
14. A unitary apparatus for evaluating characteristics of a sample
comprising: an intensity modulated excitation source for
periodically exciting a region on the surface of the sample; means
for monitoring the modulated optical reflectivity induced by said
periodic excitation and generating first output signals in response
thereto; means for obtaining X-ray reflectivity information from
the same region on the sample surface and generating second output
signals in response thereto; and a processor for evaluating the
characteristics of the sample based on a combination of the first
and second output signals.
15. An apparatus as recited in claim 14 wherein the processor uses
either of the first or second output signals to characterize one
parameter of the sample and wherein the other output signals are
used to further characterize the sample with said one parameter
being treated as a known parameter.
16. A unitary apparatus for evaluating characteristics of a sample
comprising: an intensity modulated pump beam directed to the sample
for periodically exciting a region on the surface of the sample; a
first probe beam directed to reflect off the periodically excited
region; a first detection module having a photodetector for
monitoring the modulated changes in the reflected first probe beam
induced by said periodic excitation and generating first output
signals in response thereto; a second probe beam of X-rays directed
to reflect off the same region on the sample surface; a second
detection module for monitoring the non-modulated reflected power
of the second probe beam and generating second output signals in
response thereto; and a processor for evaluating the
characteristics of the sample based on a combination of the first
and second output signals.
17. An apparatus as recited in claim 16 wherein the first detection
module monitors the modulated variations in the magnitude and/or
phase of the first probe beam.
18. An apparatus as recited in claim 16 wherein the processor uses
either of the first or second output signals to characterize one
parameter of the sample and wherein the other output signals are
used to further characterize the sample with said one parameter
being treated as a known parameter.
Description
PRIORITY
[0001] This application claims the benefit of U.S. Provisional
Application No. 60/189,334, which provisional application was filed
on Mar. 14, 2000 and is hereby incorporated by reference in its
entirety.
FIELD OF THE INVENTION
[0002] The present invention relates to the field of metrology
tools for measuring semiconductor wafers and, in particular,
relates to a tool that combines two complementary types of
measurements into a single tool to reduce ambiguities in both types
of measurements.
BACKGROUND OF THE INVENTION
[0003] The semiconductor industry has a continuing interest in
measuring various thin film layers formed on semiconductor wafers.
A number of metrology devices have been developed for making these
measurements.
[0004] One example of such an apparatus is disclosed in PCT
application WO/9902970, published Jan. 21, 1999. The assignee
herein has commercialized the device described in that patent
application under the name OPTI-PROBE 5240. This device includes a
number of measurement technologies. More specifically, the device
includes a beam profile ellipsometer (BPE) (see U.S. Pat. No.
5,181,080); a beam profile reflectometer (BPR) (see U.S. Pat. No.
4,999,014); relatively conventional broad band (BB) and deep
ultraviolet (DUV) spectrometers; a proprietary broad band
spectroscopic ellipsometer (SE) (see U.S. Pat. No. 5,877,859) and
an off-axis narrow band ellipsometer (see U.S. Pat. No. 5,798,837).
All of the above-recited patents and PCT applications are
incorporated herein by reference.
[0005] The above described system is particularly suited for
characterizing relatively transparent films, such as silicon
dioxide, on semiconductors. This measurement system is somewhat
less useful when analyzing opaque films such as metals.
[0006] An optical technique which is particularly suited for
measuring the thickness of very thin metal films is X-ray
reflectometry. Using a probe beam generated by a source of very
short wavelength radiation, thin films can be analyzed which are
opaque to both visible and UV wavelengths. One example of such a
system is described in U.S. Pat. No. 5,619,548, issued Apr. 8,
1997, and incorporated herein by reference.
[0007] In an X-ray reflectometer, a probe beam of X-ray radiation
is directed to impinge on the sample at an angle so that it is at
least partially reflected. A sample may typically consist of a
substrate covered by one or more thin metal layers. At very shallow
angles, below a critical angle (.PSI..sub.c) (as measured between
the surface of the sample and the incoming ray), all of the X-ray
radiation will be reflected. Typical incidence angles are very
shallow, near grazing incidence, because the reflectivity falls
very quickly as the angle is increased above the critical angle. As
the angle of incidence of the incoming beam increases, an
increasing amount of radiation will be transmitted through the top
metal layer and the amount of reflected light will be reduced. Some
of the radiation transmitted through the metal layer(s) will reach
the interface between the metal film and the substrate and be
reflected from the substrate. The radiation reflected at the
interfaces among the metal film layers and the substrate will
interfere, giving rise to a reflectivity curve showing interference
effects. By analyzing the dependence of the reflectivity on the
angle of incidence, one can independently determine both the
thickness and density of the thin film layers on the sample.
[0008] The added capability offered by an X-ray reflectometer has
led prior researchers to attempt to combine the measurements from
an X-ray reflectometer with those of other optical measurement
tools. For example, samples have been analyzed using a combination
of grazing X-ray reflectometry and spectroscopic ellipsometry.
(See, "A new versatile system for characterization of
antireflective coatings using combined spectroscopic ellipsometry
and grazing X-ray reflectance," Boher, SPIE, Vol. 3741, page 104,
May 1999.) Other researchers have proposed combining X-ray
reflectometry with infrared spectroscopy and transmission
spectroscopy. In addition, researchers have also discussed the
desirability of obtaining multiple separate measurements including
X-ray reflectometry, variable angle of incidence reflectometry and
"mirage" style, photo-thermal measurements to evaluate a sample.
(See, "Optical and X-ray characterization applied to multilayer
reverse engineering," Boudet, Optical Engineering, Vol. 37 (1),
page 2175, July 1998). In this paper, the authors used the
photothermal method to analyze losses from absorption.
[0009] The inventors herein have recognized that there are further
advantages to combining the measurements that can be obtained from
X-ray reflectometry with measurements that can be obtained from a
thermal and/or plasma wave analysis. A thermal and plasma wave
metrology device is marketed by the assignee herein under the name
of Therma-Probe. This device incorporates technology described in
the following U.S. Pat. Nos.: 4,634,290; 4,646,088; 5,854,710 and
5,074,669. The latter patents are incorporated herein by
reference.
[0010] In the basic device described in the patents, an intensity
modulated pump laser beam is focused on the sample surface for
periodically exciting the sample. In the case of a metal, thermal
waves are generated, while in a semiconductor, both thermal and
plasma waves are generated. These waves spread out from the pump
beam spot and reflect and scatter off various features and interact
with various regions within the sample in a way which alters the
flow of heat and/or plasma from the pump beam spot.
[0011] The presence of the thermal and plasma waves has a direct
effect on the reflectivity at the surface of the sample. Features
and regions below the sample surface which alter the passage of the
thermal and plasma waves will therefore alter the optical
reflective patterns at the surface of the sample. By monitoring the
changes in magnitude and/or phase of the reflectivity of the sample
at the surface, information about characteristics below the surface
can be investigated.
[0012] In the basic device, a second laser is provided for
generating a probe beam of radiation. This probe beam is focused
colinearly with the pump beam and reflects off the sample. A
photodetector is provided for monitoring the periodic changes in
the magnitude and phase of the reflected probe beam. The
photodetector generates an output signal which is proportional to
the reflected power of the probe beam and is therefore indicative
of the varying optical reflectivity of the sample surface.
[0013] The output signal from the photodetector is filtered to
isolate the changes which are synchronous with the pump beam
modulation frequency. In the preferred embodiment, a lock-in
detector is used to monitor the magnitude and phase of the periodic
reflectivity signal. This output signal is conventionally referred
to as the modulated optical reflectivity (MOR) of the sample.
[0014] This system has been used successfully to measure ion
implantation levels in semiconductors. Such a system can also be
used to measure thermal conductivity or thermal diffusion in a thin
film layer on a sample (see U.S. Pat. No. 5,074,669, incorporated
by reference). Such a system can also be used to measure
characteristics of thin metalized layers (see U.S. Pat. No.
5,978,074, incorporated by reference).
[0015] Other techniques besides modulated optical reflectivity
detection can be used to monitor the effects of thermal and plasma
wave propagation in a sample. For example, various interferometry
and mirage effects techniques have been used. The broad scope of
the subject invention includes these techniques as well. (See for
example, U.S. Pat. No. 6,108,087).
[0016] Since an X-ray reflectometer measurement permits
determination of both thickness and density independently, it has
been recognized by the inventors herein that special benefits can
be obtained by analyzing a sample using a combination of X-ray
reflectometry along with a thermal and plasma wave measurement
technique. More specifically, if information about the thickness
and/or density of the thin film can be obtained using an X-ray
reflectometer measurement, the remaining variables (such as the
index of refraction and thermal conductivity) can be more easily
determined with a thermal wave tool since one less variable needs
to be resolved through the analysis of the data.
SUMMARY OF THE INVENTION
[0017] Accordingly it is an object of this invention to provide a
measurement device that includes both an X-ray reflectometer and a
thermal and plasma wave measurement module for determining the
characteristics of a sample. Preferably, these two measurement
modules are combined into a unitary apparatus and arranged to be
able to take measurements at the same location on the wafer. A
processor will receive data from both modules and combine that data
to resolve ambiguities about the characteristics of the sample. The
processor can either be part of the unitary apparatus or separate
therefrom as long as the measurement data is transferred to the
processor. In either case, the apparatus is unitary so long as the
X-ray reflectometer and the thermal and/or plasma wave measurement
modules are combined into a single device.
BRIEF DESCRIPTION OF THE FIGURES
[0018] FIG. 1 is a composite block and schematic diagram of an
apparatus for carrying out the detection of thermal and plasma
waves in accordance with the subject invention.
[0019] FIG. 2 is a composite block and schematic diagram of an
apparatus for carrying out X-ray reflectometric measurements in
accordance with the subject invention.
[0020] FIG. 3 is a composite block and schematic diagram of a
unitary apparatus for carrying out both X-ray reflectometric
measurements and thermal wave measurements in accordance with the
subject invention.
DETAILED DESCRIPTION OF THE INVENTION
[0021] The subject combination can be used effectively on samples
with complex multilayer samples. For example, consider a silicon
wafer upon which has been deposited a thin layer of tantalum
nitride (250 Angstroms) covered by a relatively thicker layer of
copper (2000 Angstroms or greater). Tantalum nitride is a
relatively opaque metallic material. For such a sample, an X-ray
reflectometer measurement would be able to accurately determine the
thickness of the thin intermediate layer of tantalum nitride. This
is so because the X-rays will penetrate the copper and reflect off
the tantalum nitride. The interference fringes can then be analyzed
to determine layer thicknesses. In addition, the X-ray reflectance
measurements can also provide information about the density of the
top copper layer. However, the X-ray reflectance measurements can
less easily determine the thickness of the copper layer since any
interference fringes associated with that layer would be too
closely spaced together to allow resolution. Nonetheless, the
thickness of the thicker copper layer can easily be measured using
a thermal wave analysis. The tantalum nitride layer will
essentially be invisible to the thermal wave analysis. By combining
the two measurements in a single tool, the user can more readily
obtain a greater amount of information about the multilayer
structure.
[0022] In addition, thermal wave measurements can also be used to
determine the diffusivity of a layer. Diffusivity is a function of
the thermal conductivity, density, and the specific heat of the
material. For most materials, the specific heat does not vary
significantly within a given layer. As noted above, X-ray
reflectometry can be used to determine the density of a layer.
Thus, by combining X-ray reflectometry measurements (which enable a
density analysis) with thermal wave measurements (which enable a
diffusivity analysis), the thermal conductivity of the layer can be
determined even if the thickness of the layer is unknown. It is
also possible to evaluate sheet resistance based on the calculated
thermal conductivity of the material.
[0023] Another advantage of the subject combination relates to
product wafer measurement capability. It is known that the
assignee's Therma-Probe system can measure on product wafers with
small feature sizes. In part this capability arises from the
smallness of the focused pump and probe beam spot size on the
sample in conjunction with accurate wafer positioning controls.
While the X-ray reflectometry spot tends to be significantly larger
than the thermal wave test spot, it has been shown by the assignee
herein that the X-ray interaction can also be used on product
wafers. This relationship is described in co-pending application
Ser. No. 09/629,407, filed Aug. 1, 2000, and incorporated herein by
reference. In brief, it has been found that the X-rays do not
scatter very strongly when interacting with structures found on
product wafers. Therefore, using a proper analysis an X-ray
reflectometer can characterize blanket film structures deposited on
a product wafer almost as easily as if the wafer were a test wafer.
Since both of these technologies can provide information about
product wafers, the combination can be used to further analyze
structures on product wafers thereby minimizing the need for test
wafers.
[0024] Providing multiple measurement tools in a single device has
added benefits. For example, it is possible to arrange the optical
systems to measure on the same point on the wafer without moving
the wafer. In addition, a single tool has a smaller footprint and
therefore takes up less floor space in the semiconductor
fabrication facility. By combining technologies in a single tool,
costs can be reduced by eliminating duplicate subsystems such as
wafer handlers and computers. Finally, the combination can simplify
and streamline decision making since the information from the two
measurement modalities can be coordinated instead of producing
conflicting results as in the prior art when two separate devices
might be used.
[0025] Further analytical capability can be obtained if the device
is arranged to include additional measurement modalities. Such
additional measurement modalities can include one or more optical
metrology devices of the type found in the assignee's OPTI-PROBE
5240, discussed above.
[0026] Referring to FIG. 1, there is illustrated an apparatus 20
for monitoring thermal and plasma waves. The apparatus of FIG. 1
illustrates only the basic elements. Those skilled in the art will
understand that a commercial devices will be more complex. More
details of a thermal wave system are disclosed in U.S. Pat. No.
5,978,074, cited above.
[0027] As seen in FIG. 1, a sample 22 rests on a platform 24.
Platform 24 is capable of movement in two orthogonal directions in
a manner such that the sample can be rastered with respect to the
heating and probe beams of the subject invention.
[0028] The means for generating thermal and plasma waves includes a
laser 30 emitting a beam 34 which is intensity modulated by
modulator 32. In the preferred embodiment, beam 34 is focused on
the surface of the sample by a microscopic objective 38. Beam 34 is
intended to periodically excite the sample surface. This periodic
excitation is the source of thermal and plasma waves that propagate
outwardly from the center of the beam. The plasma and thermal waves
interact with sample boundaries and barriers in a manner that is
mathematically equivalent to scattering and reflection of
conventional propagating waves. Any features on or beneath the
surface of the sample that have thermal or plasma diffusion
characteristics different from their surroundings will reflect and
scatter thermal and plasma waves and thus become visible to these
waves.
[0029] The detection system includes a laser 50 for emitting a
probe beam 52. Probe beam 52 is directed onto a region of the
sample surface that has been periodically heated by the modulated
energy beam 34. Probe beam 52 is first passed through a polarizing
splitter 54 oriented in a manner such as to let the coherent light
emanating from laser 50 to pass freely therethrough. The splitter
will, however, deflect all light whose phase has been rotated
through 90 degrees relative to beam 52. The reason for this
arrangement will become apparent below.
[0030] Light probe beam 52 is then passed through a
1/4.lambda.-waveplate 55. Waveplate 55 functions to rotate the
phase of the probe beam by 45 degrees. As can be appreciated, on
the return path of the beam, the waveplate will rotate the phase of
the beam another 45 degrees so that when it reaches splitter 54 the
phase of the beam will have been rotated a total of 90 degrees from
the incoming orientation. By this arrangement, the splitter 54 will
deflect the retro-flected light beam up to detector 56.
[0031] After the probe beam 52 initially passes through waveplate
55, it is reflected downwardly by dichroic mirror 36. The dichroic
mirror is selected to be transparent to the pump beam wavelength
and reflective of the probe beam wavelength. In the preferred
embodiment, the pump beam and the probe beam are aligned in such a
manner that they are directed in a coincident manner down through
lens 38 and focused at the same spot on the surface of the sample.
By focusing the pump and probe beams at the same spot, the maximum
signal output can be achieved.
[0032] The probe beam is reflected back up to the dichroic mirror
where it is, in turn, reflected back along the incoming path and
through the 1/4 .lambda.-waveplate 55. As discussed above,
waveplate 55 rotates the phase of the probe beam by another 45
degrees such that when the beam reaches splitter 54, its phase has
been rotated 90 degrees with respect to the original beam.
Accordingly, this splitter will deflect the retro-reflected probe
beam upwardly towards detector 56.
[0033] Since intensity variations of a radiation beam are to be
detected, a standard photodetector may be employed as a sensing
mechanism. The intensity variations which are measured are then
supplied as an output signal to a processor for deriving the data
on the thermal and plasma waves based on the changing surface
temperature conditions as indicated by the changing output
signal.
[0034] The operation of processor 58 is dependent on the type of
testing configuration which is utilized. In all cases, the
processor is designed to evaluate the intensity changes of the
incoming probe beam which are the result of the periodic
reflectivity changes caused by the periodic heating on the sample.
These periodic intensity changes are filtered to produce a signal
which may be evaluated. Details of a suitable detector and
processor arrangement are disclosed in U.S. Pat. No. 5,978,074. The
latter patent also discloses how thermal waves can be detected by
monitoring the periodic angular deflections of a probe beam. As
noted above, other techniques are known for thermal wave
measurements including the mirage technique and interferometric
techniques. (See for example, the articles cited of record in U.S.
Pat. No. 4,521,118)
[0035] A preferred XRR technique for use in the subject combination
is described in U.S. Pat. No. 5,619,548, issued Apr. 8, 1997, which
is hereby incorporated by reference in its entirety. FIG. 2
illustrates the basic components for this technique. More details
of a suitable XRR system can be found in U.S. Ser. No. 09/527,389,
filed Mar. 16, 2000.
[0036] Referring to FIG. 2, the X-ray scattering system includes an
X-ray source 31 producing an X-ray bundle 33 that comprises a
plurality of X-rays shown as 35a, 35b, and 35c. An X-ray reflector
37 is placed in the path of the X-ray bundle 33. The reflector 37
directs the X-ray bundle 33 onto a test sample 39 held in a fixed
position by a stage 45, and typically including a thin film layer
41 disposed on a substrate 43. Accordingly, a plurality of
reflected X-rays, 57a, 57b, and 57c (forming bundle 46)
concurrently illuminate the thin film layer 41 of the test sample
39 at different angles of incidence. The X-ray reflector 37 is
preferably a monochromator. The diffraction of the incident bundle
of X-rays 33 within the single-crystal monochromator allows only a
narrow band of the incident wavelength spectrum to reach the sample
39, such that the Bragg condition is satisfied for this narrow
band. As a result, the plurality of X-rays 57a, 57b, and 57c, which
are directed onto the test sample 39, are also monochromatic. A
detector 47 is positioned to sense X-rays reflected from the test
sample 39 and to produce signals corresponding to the intensities
and angles of incidence of the sensed X-rays. A processor 60 is
connected to the detector to receive signals produced by the
detector in order to determine various properties of the structure
of the thin film layer, including thickness, density and surface
roughness.
[0037] In a basic system, a probe beam of X-ray radiation is
directed to strike the sample at an angle selected so that it is at
least partially reflected. A sample may typically consist of a
substrate covered by one or more thin metal layers. At very shallow
angles, below a critical angle (.PSI..sub.c) (as measured between
the surface of the sample and the incoming ray), all the X-ray
radiation will be reflected. As the angle of incidence of the
incoming beam increases with respect to the sample surface, an
increasing amount of radiation will be transmitted through the top
metal layer and the amount of reflected light will be reduced. Some
of the radiation transmitted through the metal layer(s) will reach
the interface between the metal film and the substrate and be
reflected off the substrate.
[0038] The radiation reflected at the interfaces among the metal
film layers and the substrate will interfere, giving rise to a
reflectivity curve showing interference effects.
[0039] For a given sample of thin films, X-ray reflectivity can be
determined using a Fresnel equation modeling as a function
principally of X-ray wavelength (.lambda.), angle of incidence, and
the thicknesses and optical properties of the materials making up
the layers. Typically the critical angle at which total reflection
occurs is quite small (.about.0.1-0.5.degree.). Because
reflectivity falls very quickly as the angle of incidence is
increased above the critical angle, small angle X-ray reflection is
experimentally important. Under a small angle approximation (sin
.PSI..congruent..PSI.), a recursive formula for the X-ray
reflectivity at an interface between a layer n-1 and a layer n is
given by 1 R n - 1 , n = a n - 1 4 ( R n , n + 1 + F n - 1 , n R n
, n + 1 F n - 1 , n + 1 ) ,
[0040] where
F.sub.n-1,n=(f.sub.n-1-f.sub.n)/(f.sub.n-1+f.sub.n),
[0041] and where
a.sub.n=exp((-i.pi./.lambda.)f.sub.nd.sub.n).
[0042] Here d.sub.n is the thickness of layer n and .PSI..sub.c(n)
is the critical angle at which total reflection occurs for X-rays
of wavelength .lambda. incident on material of layer n.
[0043] The f.sub.n are given by
f.sub.n=A.sub.n-iB.sub.n,
[0044] where
A.sub.n=(1/{square root}{square root over
(2)})({[.PSI..sup.2-.PSI..sub.c.-
sup.2(n)].sup.2+4.beta..sub.n.sup.2}.sup.1/2+[.PSI..sup.2-.PSI..sub.c.sup.-
2(n)]).sup.1/2
B.sub.n=(1{square root}{square root over
(2)})({[.PSI..sup.2-.PSI..sub.c.s-
up.2(n)].sup.2+4.beta..sub.n.sup.2}.sup.1/2-[.PSI..sup.2-.PSI..sub.c.sup.2-
(n)]).sup.1/2,
[0045] and where
[0046] .beta..sub.n=.lambda..mu..sub.n/4.pi., .PSI. is the angle of
incidence of the X-rays, and .mu..sub.n is the linear absorption
coefficient of the layer n.
[0047] These recursive equations are solved by setting R.sub.N, N+1
equal to 0 with layer n=N corresponding to the substrate and
carrying out the resulting recursive calculations, starting at the
bottom of the thin film stack. With layer n=1 corresponding to the
vacuum, the product (.vertline.R.sub.1,2.vertline..sup.2) of
R.sub.1,2 with its complex conjugate gives the ratio of the
reflected X-ray intensity to incident X-ray intensity.
[0048] The theoretical modeling of X-ray reflection based on the
classical Fresnel equations, as well as complications from the
width of interfaces and microscopic surface roughness, are
discussed in greater detail in the following references, each of
which is hereby incorporated by reference in its entirety: L. G.
Parratt, Phys. Rev. 95, 359 (1954); C. A. Lucas et al., J. Appl.
Phys. 63, 1936 (1988); M. Toney, S. Brennan, J. Appl. Phys. 66,
1861 (1989).
[0049] One approach to measuring the film thicknesses of patterned
semiconductor wafers using XRR relies on the recognition that the
measured X-ray reflection curve can be attributed primarily to the
thicknesses of the layers rather than the structure of the pattern.
The wavelength of the X-rays used in the XRR measurement is on the
order of a few angstroms. Compared to the feature size of the
patterned wafers, which is on the order of 10,000 angstroms, the
wavelength is very small. Therefore interference effects from the
structure of the pattern itself are not important. The most
noticeable effect is that the reflected X-ray intensity may be
generally reduced since the portion of the light that is incident
onto the sides and bottoms of the recesses contributes less to the
reflected signal. When the depth of the recesses is large compared
to the thickness of the layers being measured, one sees only minor
changes in the X-ray reflectivity curve beyond the reduction in
overall intensity.
[0050] As used herein, "patterned wafer" or "patterned
semiconductor wafer" means a semiconductor wafer whose surface
bears an artificial pattern whose features are small in size
relative to the spot size of the X-ray probe beam. As noted above,
typically, the measurement spot size for the probe beam is one
millimeter or larger, while the features of the pattern are on the
order of one micron in size, and even the test sites on a patterned
wafer have dimensions typically smaller than 100 microns. Thus,
there is typically at least an order of magnitude separating the
X-ray probe beam spot size and the size of even the test sites on
the patterned wafer.
[0051] Because of the similarity in shape of the X-ray reflectance
curves, analysis of the X-ray reflectivity curve for a patterned
wafer can be greatly simplified through comparison with
measurements made on an unpatterned wafer having similar layers.
The unpatterned comparison wafer could be simply an unpatterned
region on the patterned wafer, which unpatterned region underwent
similar deposition as the patterned region.
[0052] In the case of the patterned wafer data, a simple
transformation is applied based on the close resemblance of the
patterned wafer reflectivity curve RP(.theta.) and the unpatterned
wafer reflectivity curve RU(.theta.). (Here .theta. is the angle of
incidence, but other dependent variables, such as the wave vector
transfer, could also be used.) A transformation function T(.theta.)
is chosen such that RP(.theta.).times.T(.theta.) closely
approximates RU(.theta.). The resemblance of RP(.theta.) and
RU(.theta.) is such that T(.theta.) may appropriately be a simple
linear function of .theta.. However, more complex functions could
also be chosen so that, for example, T(.theta.) could appropriately
be a quadratic or cubic function of .theta. or a "splicing" of such
functions for different portions of the angular spectrum.
[0053] Using a simple linear transformation function, T(.theta.),
the data for the patterned wafer can be transformed. The same
Fresnel equation modeling that are applied to an unpatterned wafer
can be applied to the transformed reflectivity data to find the
layer thicknesses for a patterned wafer. The necessary parameters
can be found through an iterative nonlinear least squares
optimization technique such as the well-known Marquardt-Levenberg
algorithm. A suitable iterative optimization technique for this
purpose is described in "Multiparameter Measurements of Thin Films
Using Beam-Profile Reflectivity," Fanton et al., Journal of Applied
Physics, Vol. 73, No. 11. p. 7035 (1993) and "Simultaneous
Measurement of Six Layers in a Silicon on Insulator Film Stack
Using Spectrophotometry and Beam Profile Reflectometry," Leng et
al., Journal of Applied Physics, Vol. 81, No. 8, p. 3570 (1997).
These two articles are hereby incorporated by reference in their
entireties.
[0054] Once the layer thickness is determined, one can then analyze
the full R-.PSI. curve and obtain values for density and surface
and interface roughness.
[0055] Another approach to finding the layer thicknesses for an
unpatterned wafer is to use a Fourier transform analysis. Fourier
transform analysis was applied to find layer thicknesses of polymer
systems in Seeck et al, Appl. Phys. Lett. 76, 2713 (2000), hereby
incorporated by reference in its entirety.
[0056] In another approach, when different fringe regimes are
discernible in the data, the thicknesses of the metal films on a
patterned wafer can be determined by reference to a modified Bragg
equation as follows:
sin.sup.2.PSI..sub.i=sin.sup.2.PSI..sub.c+(i+1/2).sup.2(.lambda./2d).sup.2
[0057] where ".PSI..sub.i" is the angle at which there is a fringe
maximum, .PSI..sub.c is the critical angle, i is a positive integer
with values 1, 2, 3, . . . , .lambda. is the X-ray wavelength, and
d is the layer thickness.
[0058] Since .PSI..sub.i and .PSI..sub.c are very small angles, and
since the modified Bragg equation must be valid for all critical
angles, including .PSI..sub.c=0, under this approximation the
angular spacing between adjacent interference fringes is a constant
for a given thickness d and is given by:
.DELTA..PSI.=.lambda./2d
[0059] Using this approach, a thickness
d(.DELTA..PSI.)=.lambda./(2.DELTA.- .PSI.) can be associated with
each fringe spacing in the curve. Since the approximative Bragg
equation becomes more valid as the angle of incidence increases, an
asymptotic analysis can be applied to find the true thickness d by
plotting the values for d(.DELTA..PSI.) as a function of increasing
.theta. and extrapolating the asymptote.
[0060] In the preferred embodiment, the two different measurement
modalities represented by FIGS. 1 and 2 would be arranged so that
the both measurements could easily be made in the same region of
the sample. Typically, the measurements would be made sequentially.
Given the geometries of the techniques, it would be possible to
arrange the optical elements so that only a single stage is
necessary. More particularly, and as shown in simplified form in
FIG. 3, the pump and probe beams (34, 52) of the modulated optical
reflectivity system can be directed normal to the sample surface.
In contrast, the X-ray probe beam (bundle 46) is directed at near
grazing incidence to the sample, thus permitting both optical
systems to be arranged to measure essentially the same region on
the sample. The data from both measurement modules can be supplied
to a common processor 60 which can integrated with the same device
or located remotely from the device. Using data taken by both
modules from the same region on the sample will improve measurement
accuracy.
[0061] The scope of the present invention is meant to be that set
forth in the claims that follow and equivalents thereof, and is not
limited to any of the specific embodiments described above.
* * * * *